(b) If A(t) is the amount of the investment at time t for the case of continuous compounding, write a differential equation satisfied by A(t).

Answers

Answer 1

Answer:

[tex]A'(t) = rA(t)[/tex]

Step-by-step explanation:

Given

[tex]A(t) \to[/tex] Amount

Required

The differential equation

The equation for the amount is:

[tex]A(t) = A_0 * e^{rt}[/tex]

Where:

[tex]A_0 \to[/tex] initial amount

[tex]r \to[/tex] rate

[tex]t \to[/tex] time

Differentiate[tex]A(t) = A_0 * e^{rt}[/tex]

[tex]A'(t) = A_0 * r * e^{rt}[/tex]

So, we have:

[tex]A'(t) = rA_0 * e^{rt}[/tex]

From the question, we have: [tex]A(t) = A_0 * e^{rt}[/tex]

So, the equation becomes

[tex]A'(t) = rA(t)[/tex]


Related Questions

if a+1/a=3
What is the answer? a⁵+1/a⁵

Answers

Answer:

123

Step-by-step explanation:

We can square and cube the equation, then multiply the results together.

(a + [tex]\frac{1}{a}[/tex]) = 3 ← square both sides

a² + 2 + [tex]\frac{1}{a^2}[/tex] = 9 ( subtract 2 from both sides )

a² + [tex]\frac{1}{a^2}[/tex] = 7 → (1)

-----------------------

Now cube both sides

a³ + [tex]\frac{1}{a^3}[/tex] + 3(a + [tex]\frac{1}{a}[/tex]) = 27

a³ + [tex]\frac{1}{a^3}[/tex] + 3(3) = 27

a³ + [tex]\frac{1}{a^3}[/tex] + 9 = 27 ( subtract 9 from both sides )

a³ + [tex]\frac{1}{a^3}[/tex] = 18 → (2)

------------------------------

Multiply (1) and (2)

(a² + [tex]\frac{1}{a^2}[/tex] )(a³ + [tex]\frac{1}{a^3}[/tex] ) = 7(18)

[tex]a^{5}[/tex]  + ( [tex]\frac{1}{a}[/tex] + a) + [tex]\frac{1}{a^5}[/tex] = 126

[tex]a^{5}[/tex] + 3 + [tex]\frac{1}{a^5}[/tex] = 126 ( subtract 3 from both sides )

[tex]a^{5}[/tex] + [tex]\frac{1}{a^5}[/tex] = 123

Please help out need explanation so I can know how to do it

Answers

Answer:

B = 60in^2

H = 4in

P = 34in

SA = 280

Step-by-step explanation:

Base - The base I assume would be the red rectangle, and 12x5 would be the area of that, so the answer is 60

Height - I assume that the height is 12, if the prism is vertical, if horizontal, then the height would be 4.

Perimeter - The length of the side lengths, so the base is the red sqaure 12+12+5+5=34

Surface Area - Base=60*4 (There are 4 "bases") =240, and then we have 5*4 (For the little squares, and times this by 2 becasue there are 2 of them) = 20*2=40

40+240=280

Solve the equation for all values of x.
-x(x – 8)(x² + 25) = 0
From deltamath.com

Answers

Answer:

x=0   , x=8 , x = ±5i

Step-by-step explanation:

-x(x – 8)(x² + 25) = 0

Using the zero product property

-x =0   x-8 =0  x^2+25 =0

x =0    x= 8     x^2 = -25

x=0    x= 8    sqrt(x^2) = sqrt(-25)

                      x = ±5i

evaluate each expression below

Answers

Answer:

see below

Step-by-step explanation:

0/7 = 0

We can divide 0 by a non zero number

5/0 = undefined

We cannot divide by 0

Lem is playing a board game and needs to roll two dice and get a six on both die in order to win the game. What is the probability that Lem will win the game on the next roll? Write your answer as a simplified fraction.

Answers

The probability of getting a 6 on one dice is 1/6

The probability of getting a 6 on both dice would be 1/6 x 1/6 = 1/36

Answer: 1/36

The definition of parallel lines requires the undefined terms line and plane, while the definition of perpendicular lines requires the undefined terms of line and point. What characteristics of these geometric figures create the different requirements?

Answers

Answer:

Parallel lines never intersect, but they must be in the same plane. The definition does not require the undefined term point, but it does require plane. Because they intersect, perpendicular lines must be coplanar; consequently, plane is not required in the definition.

Step-by-step explanation:

Its correct trust me.

Answer:

Parallel lines never intersect, but they must be in the same plane. The definition does not require the undefined term point, but it does require plane. Because they intersect, perpendicular lines must be coplanar; consequently, plane is not required in the definition.

Step-by-step explanation:

If m={prime integers between 1 and 11}
N={Factor of 12} find
1. MuN
2.MnN​

Answers

M = {2, 3, 5, 7} (and possibly includes 11 if "between x and y" means to include both x and y)

N = {1, 2, 3, 4, 6, 12}

Then

M U N = {1, 2, 3, 4, 5, 6, 7, 12}

(or possibly {1, 2, 3, 4, 5, 6, 7, 11, 12})

M ∩ N = {2, 3}

Which of the following phrases are inequalities?
Choose 3 answers:
Choose 3 answers:

(Choice A)
A
5=\dfrac{55}{11}5=
11
55

5, equals, start fraction, 55, divided by, 11, end fraction

(Choice B)
B
-2<2\text{}−2<2minus, 2, is less than, 2, start text, end text

(Choice C)
C
10-6q10−6q10, minus, 6, q

(Choice D)
D
7w>5.6\cdot 10^{4}7w>5.6⋅10
4
7, w, is greater than, 5, point, 6, dot, 10, start superscript, 4, end superscript

(Choice E)
E
f-4-7>7-4-ff−4−7>7−4−f

Answers

Answer:

B,D, and E

Step-by-step explanation:

Yes

Divide...................​

Answers

Answer:

Exact form 9/4 Mixed number form 2 1/4 decimal form 2.25

Step-by-step explanation:

Answer:2.25

Step-by-step explanation:

hope this helps

Mattie uses the discriminant to determine the number of zeros the quadratic equation 0 = 3x2 – 7x + 4 has. Which best describes the discriminant and the number of zeros?

The equation has one zero because the discriminant is 1.
The equation has one zero because the discriminant is a perfect square.
The equation has two zeros because the discriminant is greater than 0.
The equation has no zeros because the discriminant is not a perfect square.

Answers

Answer:

The equation has two zeros because the discriminant is greater than 0.

Step-by-step explanation:

3x^2 – 7x + 4

a=3   b = -7   c=4

The discriminant is

b^2 -4ac

(-7)^2 - 4(3)(4)

49 - 48

1

Since the discriminant is greater than zero, there are two real solutions

Answer:

The equation has two zeros because the discriminant is greater than 0.

Step-by-step explanation:

if 1cm on a map represents 37 1/2 km what does a length of 2/5cm on the map represent​

Answers

Answer:

15

Step-by-step explanation:

[tex]37 \frac{1}{2} \times \frac{2}{5} = \frac{75}{2} \times \frac{2}{5} = 15[/tex]


Find dy /dx of x² - 2x + 5 - 6x

Answers

Answer:

Step-by-step explanation:

If [tex]y=x^2-2x+5-6x[/tex] then

[tex]y=x^2-8x+5[/tex] by combining like terms. (I'm thinking you might have mistyped the problem because this representation is weird).

[tex]\frac{dy}{dx}=2x-8[/tex]

please help I will mark brainlyest ​

Answers

Answer:

Choice D.

Step-by-step explanation:

Hello! Me again, this is my explanation to my solution,

A stem-and-leaf plot shows the data shape and the densities of the different classes in a graphical form such that the information in the data such as the data characteristics are self displayed by the data numbers arranged in the stem-and-leaf plot. The stem-and-leaf plot keeps the raw numerical data, in the form they were obtained and by their arrangement, outliers are easily spotted.

Hope this helped! Let me know if you have further questions! :)

a giraffe can run 32 miles per hour. what is this speed in feet per second?

Answers

Answer:

46.9 ft/sec

Step-by-step explanation:

A giraffe can run 32 miles per hour. What is this speed in feet per second? Round your answer to the nearset tenth.

Can someone please explain how to do this?(Picture above) I'll give brainliest!

Answers

Answer:

f(1)=4

f(-3)=4

f(5)=-2

f(0)=2

f(-1)=0

f(3)=2

Step-by-step explanation:

Pose f(x) as your x value. Now apply to the graph

The seating capacity at a movie theater is 400. For a Monday
afternoon movie, 68% of the seats are filled. About how many
seats are empty?
-.- sorta need this answer quickly, thanks

Answers

seating capacity is 400 for a monday.

afternoon: 68% of the seats are filled

68% of 400: 272 seats left




Factor 16p4 - 24p3. find the factor

Answers

Answer:

8p^3 ( 2p -3)

Step-by-step explanation:

16p^4 - 24p^3

8*2* p^3 *p - 3*8*p^3

Factor out the common terms

8p^3 ( 2p -3)

Does this graph show a function? Explain how you know.

O A. Yes; there are no y values that have more than one x-valuer
O B. No, there are y-values that have more than one x-value.
O C. Yes, the graph passes the vertical line test.
O D. No, the graph fails the vertical line test. SUBMIT​

Answers

Answer: D) No. The graph fails the vertical line test.

Explanation:

We are able to draw a single vertical line that passes through more than one point on the red curve. For example, we could draw a vertical line through x = 5 and have it cross the red curve at (5,4) and (5,-4).

So this is one example where the graph fails the vertical line test. It passes this test when such a thing doesn't happen. In other words, a function is only possible if any x input leads to exactly one and only one y output.

In this case, x = 5 leads to multiple outputs y = 4 and y = -4 at the same time. There are other x values which this occurs as well (any x values such that x > 1). So this is why we don't have a function.

Will Give Brainliest!

Solve for r.
Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.

35r - 21 < -35r + 19

Answers

Answer:

r < 4/7

Step-by-step explanation:

35r - 21 < -35r + 19

35r + 35r < 19 + 21

70r < 40

r < 4/7

Answer:

r < 4/7

Step-by-step explanation:

Determine what type of model best fits the given situation: the temperature of a cup of coffee decreases by 5 F every 20 minutes.

A. liner
B. exponential
C. quadratic
D. none of these

Answers

Answer: T = -t / 4 + T0   where t is the temperature in minutes elapsed, T is the final temperature, and T0 is the initial temperature

Explanation: This is a linear equation in T and t

(-1 / 4 represents -5 deg / 20 min  = - 1 deg / 4min

The Coffee Counter charges ​$11

per pound for Kenyan French Roast coffee and ​$10

per pound for Sumatran coffee.
How much of each type should be used to make a 20 pound blend that sells for ​$10.60

per​ pound?

Answers

Answer:

12 pounds of Kenyan French Roast coffee

8 pounds of Sumatran coffee

Step-by-step explanation:

if you use x pounds of Kenyan French Roast coffee and y pounds of Sumatran coffee then you know that

11x + 10y = 10.6 * 20

x+y=20

10x+10y=200

11x+10y=212

x=12

y = 20-x = 20-12 = 8

so you want to use

12 pounds of Kenyan French Roast coffee

8 pounds of Sumatran coffee

A team of 5people to be selected from 7women & 6men. Find the number of different teams that could be selected if there must be more women than men in the team

Answers

Answer:

1246 teams

Step-by-step explanation:

We are told there are 7women & 6men.

If 5 people are selected and there must be more women than men in the team.

This means there must be a minimum of 3 women.

Thus;

For 3 women;

7C3 × 6C2 = 525

For 4 women;

7C4 × 6C3 = 700

For 5 women;

7C5 × 6C0 = 21

Thus;

Total = 525 + 700 + 21 = 1246 teams

Nishi invests £3500 at 4% interest per year. Work out how much she will have altogether after: 2 years​

Answers

Answer:

£3780

Step-by-step explanation:

P= £3500, R=4%, t=2years

I = PRT/100

I= (3500×4×2)/100 =£280

Amount in 2years = P+I = £3500+ £280= £3780

Hope made 3 different yo-yo's. She used 1 3/4 meters of string for the first yo-yo, 1 meter of string

Answers

Answer:

See explanation

Step-by-step explanation:

Your question is different from the attachment

Statement 1

1 adult + 5 Children

$4 for adult and total of $16 for both adult and children

Let

Cost of children skating = x

The equation is

4 + 5x = 16

Statement 2:

Cost of making a bike bag= $4

Selling price of the bike bag = $5

Profit = $16

Let x = number of bike bag

Profit = selling price - cost price

16 = 5x - 4x

16 = x(5 - 4)

Also written as

(5 - 4)x = 16

Statement 3:

Initial temperature = 16°C

Change in temperature per hour = 4°C

Final temperature = 5°C

Let

x = number of hours it changes

16 - 4x = 5

Hope made 3 different yo-yos. She used 1 3/4 meters of string for the first yo-yo, 1 meter of string for the second yo-yo, and a total of meters of string 4 1/3

length of first yo-yo = 1 3/4

length of second yo-yo = 1

Length of third yo-yo = x

Total = 4 1/3

Total length = length of first yo-yo + length of second yo-yo + length of third yo-yo

4 1/3 = 1 3/4 + 1 + x

4 1/3 = 2 3/4 + x

4 1/3 - 2 3/4 = x

13/3 - 11/4 = x

(52-33) / 12 = x

19/12 = x

x = 1 7/12

PLEASE Help! I need this by tomorrow!

Answers

Answer:

18m

Step-by-step explanation:

6 times 3 = 18

help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

-23 that’s the answer I’m pretty sure

Answer:

4

Step-by-step explanation:

1)

-2x - 5 = x - 17

-2x - 5 + 5 = x - 17 + 5

* cancel out 5 on each side of equal sign.

2)

-2x = x - 12

-2x - x = x - x - 12

* cancel out x on each side of equal sign.

3)

-3x = -12

-3x/ -3 = -12/-3

* cancel out -3x on each side of equal sign.

4) Simplify

x = 4

Hope this helps, good luck! :)

Have a great day!!

A tank is capable of holding 36,18 and 72 litres of milk . Determine which is the greatest vessel which can be uses to fill each one of them on exact number of times

Answers

Answer:

Greatest vessel to fill each in exact number of times is 6 litres

Step-by-step explanation:

To solve this, we will find the greatest common factor of 36,18 and 72

Thus;

Their prime factors are;

18: 2, 3

36: 2, 2, 3, 3,

72: 2, 2, 2, 3, 3

The factors common to all of them are 2 & 3.

Thus;

GCF = 2 × 3 = 6

express the ratio 7day to 6weeks as a decimal fraction

Answers

Answer:

6 weeks=6*7 days=42days

7/42 =1/6 =0.16667

OR

7 days=1 week

therefore 1/6=0.16667

Note that both must be in the same unit.

5. Solve each of the following quadratic equations using the Quadratic Formula (Express all roots as integers or as real numbers rounded to one decimal place)
a) 2x2 – 3x - 10 = 0
b) 3x2 - 8x + 4 = 0 (answer pls:)

Answers

The correct answer is: B

Please hurry I will mark you brainliest

Ingrid walks 1 m, and then turns 90° left. She repeats these steps three more times and returns to the exact place she started. Which of the following instructions can she repeat a number of times to arrive at the exact same starting point?

• Walk 1 m, and then turn 40° left.

• Walk 1 m, and then turn 55° left.

• Walk 1 m, and then turn 70° left.

• None of these

Answers

Answer:

• Walk 1 m, and then turn 40° left.

Step-by-step explanation:

Answer:

None of them

Step-by-step explanation:

None of the answers get her back to the same point in only four steps. she would need a different way of walking to get the same result as a square.

Other Questions
Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of y = 2x2 12x + 6. Joshua borrowed $1,400 for one year and paid $70 in interest. The bank charged him a service charge of $12. If Joshua repaid the loan in 12 equal monthly payments, what is the APR? (Enter your answer as a percent rounded to 1 decimal place.)APR% . :() ?() ?() ?() ? solution is an example of______mixtures Tina invests $3,700 into an account with a 4.4% interest that is compounded quarterly. How much money will she have inthis account if she keeps it for 8 years?Round your answer to the nearest cent.Do NOT round until you have calculated the final answer. Which value for the constant d makes x = -2 an extraneous solution in the following equation? [tex]\sqrt{6-15x} =5x+d[/tex] Draw a demand for dollars curve. Label it D. Draw a supply of dollars curve. Label it S. Draw a point at the equilibrium quantity and equilibrium exchange rate. Draw an arrow between the D and S curves that indicates a price at which there is a surplus of dollars. Label it. What happens in the foreign exchange market when a surplus of dollars exists? When there is a surplus of dollars in the foreign exchange market, _____ You have a bag which contains only red and green marbles. In this bag with $x^{2} 5$ marbles total, $x 1$ are red. Also, $x-3$ marbles have a scratch on them. The probability of drawing a red marble from the original bag is equal to that of drawing a marble with a scratch from the marbles left in the bag after twenty scratch-free marbles are taken out of the full bag. How many marbles were originally in the bag? give one subject you think you are at advantage why? Please list answers below In which instrument of the following the water works as a bulb a car moves at a speed of 40km/h. it is stopped by applying brake which produce a uniform acceleration of-0.5m/s^2. how much distance will it move before coming to stop ? plz its urgent Bangladesh has been the 7 th largest mango exporter in the world and exported 1-billion-dollar worth of vegetables across the world. Within 1000 words, discuss i) How can we internationalize our productions? ii) How can we localize our productions? Discuss some research oriented examples. Im giving out brainlist!!! I need help with the work How is the atmosphere in the countryside ? Find the slope m and y-intercept of the equation:y = (-1/5)x + 7 Head is to hat as __ is to glove.elbowhandfingerfoot URGENT HELP I REALY NEED AN EXPERT HERE Peter has been seeing a counselor